542 research outputs found
Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism
In this work we discuss the natural appearance of the Generalized Brackets in
systems with non-involutive (equivalent to second class) constraints in the
Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of
the integrability conditions leads to the reduction of degrees of freedom of
these systems and, as consequence, naturally defines a dynamics in a reduced
phase space.Comment: 12 page
Nilpotent Classical Mechanics
The formalism of nilpotent mechanics is introduced in the Lagrangian and
Hamiltonian form. Systems are described using nilpotent, commuting coordinates
. Necessary geometrical notions and elements of generalized differential
-calculus are introduced. The so called geometry, in a special case
when it is orthogonally related to a traceless symmetric form, shows some
resemblances to the symplectic geometry. As an example of an -system the
nilpotent oscillator is introduced and its supersymmetrization considered. It
is shown that the -symmetry known for the Graded Superfield Oscillator (GSO)
is present also here for the supersymmetric -system. The generalized
Poisson bracket for -variables satisfies modified Leibniz rule and
has nontrivial Jacobiator.Comment: 23 pages, no figures. Corrected version. 2 references adde
Hamilton-Jacobi approach to Berezinian singular systems
In this work we present a formal generalization of the Hamilton-Jacobi
formalism, recently developed for singular systems, to include the case of
Lagrangians containing variables which are elements of Berezin algebra. We
derive the Hamilton-Jacobi equation for such systems, analizing the singular
case in order to obtain the equations of motion as total differential equations
and study the integrability conditions for such equations. An example is solved
using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results
are compared.Comment: LaTex, 30 pages, no figure
Elementary solution to the time-independent quantum navigation problem
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realizes a required quantum process or task, under the influence of a prevailing ‘background’ Hamiltonian that cannot be manipulated. When the task is to transform one quantum state into another, finding the solution in closed form to the problem is nontrivial even in the case of timeindependent Hamiltonians. An elementary solution, based on trigonometric analysis, is found here when the Hilbert space dimension is two. Difficulties arising from generalizations to higher-dimensional systems are discussed
Verifiable conditions of -recovery of sparse signals with sign restrictions
We propose necessary and sufficient conditions for a sensing matrix to be
"s-semigood" -- to allow for exact -recovery of sparse signals with at
most nonzero entries under sign restrictions on part of the entries. We
express the error bounds for imperfect -recovery in terms of the
characteristics underlying these conditions. Furthermore, we demonstrate that
these characteristics, although difficult to evaluate, lead to verifiable
sufficient conditions for exact sparse -recovery and to efficiently
computable upper bounds on those for which a given sensing matrix is
-semigood. We concentrate on the properties of proposed verifiable
sufficient conditions of -semigoodness and describe their limits of
performance
Direct approach to the problem of strong local minima in Calculus of Variations
The paper introduces a general strategy for identifying strong local
minimizers of variational functionals. It is based on the idea that any
variation of the integral functional can be evaluated directly in terms of the
appropriate parameterized measures. We demonstrate our approach on a problem of
W^{1,infinity} weak-* local minima--a slight weakening of the classical notion
of strong local minima. We obtain the first quasiconvexity-based set of
sufficient conditions for W^{1,infinity} weak-* local minima.Comment: 26 pages, no figure
Hamilton-Jacobi Approach for First Order Actions and Theories with Higher Derivatives
In this work we analyze systems described by Lagrangians with higher order
derivatives in the context of the Hamilton-Jacobi formalism for first order
actions. Two different approaches are studied here: the first one is analogous
to the description of theories with higher derivatives in the hamiltonian
formalism according to [Sov. Phys. Journ. 26 (1983) 730; the second treats the
case where degenerate coordinate are present, in an analogy to reference [Nucl.
Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison
between both approaches is made
Hamilton-Jacobi equations and Brane associated Lagrangians
This article seeks to relate a recent proposal for the association of a
covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi
formalism for strings and branes. It turns out that since in this special case,
the Hamiltonian depends only upon the momenta of the Jacobi fields and not the
fields themselves, it is the same as a Lagrangian, subject to a constancy
constraint. We find that the associated Lagrangians for strings or branes have
a covariant description in terms of the square root of the same Lagrangian. If
the Hamilton-Jacobi function is zero, rather than a constant, then it is in in
one dimension lower, reminiscent of the `holographic' idea. In the second part
of the paper, we discuss properties of these Lagrangians, which lead to what we
have called `Universal Field Equations', characteristic of covariant equations
of motion.Comment: 23 pages,LaTeX2e, clarified text, generalised proof in appendi
General Relativity in two dimensions: a Hamilton-Jacobi constraint analysis
We will analyze the constraint structure of the Einstein-Hilbert first-order
action in two dimensions using the Hamilton-Jacobi approach. We will be able to
find a set of involutive, as well as a set of non-involutive constraints. Using
generalized brackets we will show how to assure integrability of the theory, to
eliminate the set of non-involutive constraints, and to build the field
equations
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